a
Magnetic field due to straight wire $ = \,\frac{{{\mu _0}{I_e}}}{{2\pi H}}$
Magnetic field due to circular wire $ = \,\frac{{{\mu _0}{I_c}}}{{2R}}$
Now $\frac{{{\mu _0}{I_e}}}{{2\pi H}} = \frac{{{\mu _0}{I_c}}}{{2R}}$
$ \Rightarrow \,\,H = \frac{{R{I_e}}}{{\pi {I_c}}}$